Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part I — Horizontal TTI layer

Abstract

One of the distinctive features of mode-converted waves is their asymmetric moveout (i.e., the PS-wave traveltime in general is different if the source and receiver are interchanged) caused by lateral heterogeneity or elastic anisotropy. If the medium is anisotropic, the PS-wave moveout asymmetry contains valuable information for parameter estimation that cannot be obtained from pure reflection modes. Here, we generalize the so-called [Formula: see text] method, which is designed to replace reflected PS modes in velocity analysis with pure (unconverted) SS-waves, by supplementing the output SS traces with the moveout-asymmetry attributes of PS-waves. The time-asymmetry attribute [Formula: see text] is computed in the slowness domain as the difference between the paired traveltimes of the PS arrivals corresponding to ray parameters (horizontal slownesses) of equal magnitude but opposite sign. Another useful asymmetry attribute is the offset [Formula: see text] of the PS-wave traveltime minimum on a common-midpoint (CMP) gather. We demonstrate the effectiveness of the developed algorithmand the importance of including the asymmetry attributes of PS-waves in anisotropic velocity analysis for a horizontal transversely isotropic layer with a tilted symmetry axis (or TTI) medium. Simple analytic expressions for the moveout asymmetry of PSV-waves, derived in the weak-anisotropy approximation, are verified by anisotropic ray tracing. The attribute [Formula: see text] is proportional to the anellipticity parameter [Formula: see text] and reaches its maximum when the symmetry axis deviates by 20°–30° from the vertical or horizontal direction. All relevant parameters of a TTI layer can be estimated by a nonlinear inversion of the NMO velocities and zero-offset traveltimes of PP- and SS- (SVSV) waves combined with the moveout-asymmetry attributes of the PSV-wave. The inversion of pure-mode (PP and SS) moveouts alone is nonunique, while the addition of the attributes [Formula: see text] and [Formula: see text] yields stable parameter estimates from 2D data acquired in the vertical symmetry-axis plane. If the TTI model is formed by obliquely dipping fractures, the anisotropic parameters can be inverted further for the fracture orientation and compliances.